Study of trap levels in β-Ga₂O₃ by thermoluminescence spectroscopy

Ga₂O₃ belongs to the Transparent Semiconducting Oxide (TSO) group with a wide bandgap (E_g = 4.5-4.9) that makes it an excellent candidate for various optoelectronic applications. It can form different types of polymorphs, σ, β, γ, δ, and ɛ.¹ β-Ga₂O₃ is the most stable and well-studied phase; it has a monoclinic structure and belongs to the space group C2/m.² The main interest in Ga₂O₃ arises from its potential applications in devices. It is emerging as one of the strongest candidates for high power devices.^3–5 The need for more stable and more efficient power devices with high power, high break-down voltage, and large current density requires an alternative of the conventional bandgap material, and it has been shown that the performance of the power devices based on SiC and GaN semiconductors can far exceed that of conventional Si-based ones. However, SiC/GaN bulk crystals cannot be grown by atmospheric melt growth methods that are usually used for the mass production of semiconductor crystals. In contrast, β-Ga₂O, which has a much larger bandgap and higher theoretical Baliga's Figure of Merit (FOM) than SiC or GaN, can be produced by several melt growth methods, therefore, suitable for mass production.⁶ 

Native defects have significant effects on the electronic properties of semiconductors. Thus, it is imperative to understand the nature and origins of electronic defects in Ga₂O₃ which can significantly affect its optical and electrical properties.^7–12 There have been various attempts to identify the structural and electronic defects in β-Ga₂O₃ grown by different techniques,^13–18 Zhang et al. reported several deep level electronic defects in undoped β-Ga₂O₃ (010) bulk substrates using deep level optical spectroscopy (DLOS) and deep level transient spectroscopy (DLTS) measurements. Varley et al.¹⁹ investigated hydrogenated cation vacancies in β-Ga₂O₃ and found that V_Ga can form strongly bound complexes with hydrogen impurities. Despite these insightful studies, a rigorous investigation is still needed to characterize the trap levels in the bandgap of β-Ga₂O₃. In this work, thermoluminescence (TL) spectroscopy was used in conjunction with Hall effect measurements to determine the trap levels (E_D) and their effect on the transport properties in undoped, Fe-, Sn-, and Mg-doped β-Ga₂O₃ single crystals grown by different techniques. Thermoluminescence spectroscopy has shown to be an excellent technique to determine the thermal activation energy of shallow and deep level electronic defects.^20–22 One of the authors of this work has established TL as an effective tool to measure deep and shallow traps in wide bandgap oxides such as yttrium aluminum garnets^20,21 and recently used it to calculate the donor ionization energies in ZnO.²³ However, to our knowledge, no TL study of electronic defects in β-Ga₂O₃ single crystals was carried out. In the current work, ultraviolet–visible (UV-Vis) spectroscopy was also used to compare the bandgap edge of Ga₂O₃ samples, which is necessary for an accurate investigation of trap levels.

High quality undoped, Fe-doped, and Sn-doped β-Ga₂O₃ single crystals were obtained from Tamura Inc., Japan. The crystals were grown by the Edge-defined Film-fed Growth (EFG) method²⁴ propagating parallel to the (010) plane and cut into pieces of (15 ± 0.3 mm × 10 ± 0.3 mm × 0.5 ± 0.02 mm). Mg-doped β-Ga₂O₃ single crystals were obtained from another commercial supplier, which were produced by the Czochralski (CZ) method. The samples’ size was of 14.18 mm diameter and 1.20 mm thickness. A few samples were air-annealed at 900 °C for 4 h. Optical absorption spectra were recorded at room temperature using a PerkinElmer ultraviolet–visible–near infrared (UV Vis-NIR) spectrometer covering from 1100 nm to 190 nm. The scan speed and slit width for the experiments were set as 240 nm/min and 1 nm, respectively.

TL measurements were performed using an in-house built spectrometer described in detail elsewhere.^20,21,23 The measurements were carried out from −190 °C to 400 °C. The samples were first placed in a dark compartment and irradiated with UV light using a pulsed Xenon lamp at −190 °C for 30 min. Liquid nitrogen and a digital temperature regulator were used to accurately control the temperature. After irradiation, the temperature of the samples was set to increase at constant rates (60°C/min for our calculation) and the emission spectra were recorded from 200 to 800 nm at each 5 min interval.

Van der Pauw Hall-effect measurements were performed using the MMR Hall measurement system to determine the electrical transport properties of the samples. The measurements were carried out at room temperature (298 K) and at a constant magnetic field of 9300 G. Four indium contacts were made in a square arrangement on the surface of each sample and carefully adjusted to keep the contacts as small as possible.

TL is the emission of light from a sample upon thermal stimulation after irradiating the sample by ionizing radiation. The phenomena, although still not fully understood, can be explained by the energy band theory of solids.²⁵ At lower temperatures, most of the electrons reside in the valence band in an ideal semiconductor or insulator material. Electrons can be lifted up to the conduction band upon excitation. Wide bandgap materials often have structural defects or impurities that create localized energy levels in the bandgap and electrons can occupy these intermediate energy levels upon excitation by ionizing radiation. These energy levels are not delocalized and are potential traps for electrons. Thermal stimulation can release the electrons from these traps where they are transferred to the recombination center that is mostly a hole trap. Luminescence emission occurs if the recombination is radiative. The process can be summarized by the following schematic diagram (Fig. 1).

Bos explained the simplified one-trap one-center model in detail.²⁵ The mathematical model of TL can be constructed from the Arrhenius equation which states the probability of the release of an electron from a trap per unit time,

where P is the probability of electron release per unit time, s is the frequency factor and is considered as a constant in simplified model, T is the absolute temperature, k is Boltzman constant, and E_D is the thermal activation energy which is defined as the energy difference between the defect energy level and conduction band minimum. The path for trapped electrons to recombine with the center is always open but the probability is low at a lower temperature. Since the material is exposed to irradiation at low temperature, the relaxation is slow and this nonequilibrium state becomes metastable that will exist for an indefinite time until thermal stimulation is provided. Assuming that recombination is radiative and every recombination will produce one photon of a specific wavelength depending on the nature of defects and recombination center, TL intensity can be expressed as

where m is the concentration of holes trapped in a recombination center, A is the recombination probability, N is the concentration of electron trap, n is the concentration of trapped electrons at time t, A_r is the probability of re-trapping, and other parameters convey the same meaning as before. Randall and Wilkins simplified this model by assuming negligible re-trapping, linear heating rate, and formulated the well-known Randall–Wilkins first order expression for TL intensity²⁵ 

Here, n₀ is the total number of trapped electrons at time t = 0 and β is the constant heating rate. Initially, the intensity of glow peak is dominated by the first exponential half of this equation and the last half can be negligible. As a result, if ln(I) is plotted as a function of $1T$ for the first 10% of the maximum intensity of the glow peak, a straight line is obtained with the slope $−EDk$ from which activation energy, E_D, can be calculated. This is known as the initial rise method. Garlick and Gibson derived a similar equation for the second order kinetics where significant re-trapping occurs.²⁶ They assumed that the trap is far from saturated and $mA<<(N−n)Ar$⁠.

It is clear from this equation that the glow peak for the second order kinetic is almost symmetrical with the higher temperature side slightly broader than the lower temperature side and the previously described initial rise method for the calculation of activation energy can also be used here for second order kinetics.

At temperature T_m, the temperature at which the intensity of the glow peak is maximum, (dI/dT) of Eq. (3) for the first order kinetics becomes zero and we find

For two different heating rates β₁ and β₂, Eq. (5) can be modified as

Therefore, activation energy, E_D, can also be determined by heating the sample at different constant heating rates, which will shift the peak temperature, T_m. However, this different heating rate method is only applicable for first order kinetics.

In this study, the initial rise method was used to calculate the thermal activation energies of the defects since this method can be used for both first and higher order kinetics. As we will see later, our glow curve peaks are broad and hence unlikely to follow the first order kinetic where the second half of the peak curve should decay sharply because of the absence of retrapping. Some peaks overlap with each other and are found to be less sensitive toward different heating rates, and therefore would produce a large error in calculation.

Figure 2 shows the optical absorbance spectra of undoped and doped β-Ga₂O₃ single crystals grown by different techniques. Figure 2(a) shows the absorbance spectra of Fe-doped, undoped, and Sn-doped β-Ga₂O₃ single crystals grown by the EFG method. Although all the samples show almost the same band edge at 272 nm, their transparency is different at longer wavelengths. Fe-doped β-Ga₂O₃ single crystal exhibits a higher degree of transmittance than undoped or Sn-doped samples in the near IR and visible region. Mg-doped CZ grown β-Ga₂O₃ [Fig. 2(b)] shows higher absorbance in the blue region which is responsible for the yellow-brown coloration of the samples. Two samples that were doped with different concentrations of Mg have been analyzed and found to have the same band edge. However, doping concentration affects the transmittance of the samples in the near IR and visible region.

The following equation

and the Tauc equation

were used to calculate the optical bandgap, E_g, of the samples, where $α$ is the absorption coefficient, t is the thickness of the sample, and r is a constant that has a value of ½ for direct bandgap and 2 for indirect bandgap. β-Ga₂O₃ has an indirect bandgap slightly smaller than the direct bandgap; however, the weak indirect transition makes it an effectively direct bandgap material.²⁷ Hence r = 1/2 was used and $(αhν)2$ was plotted as a function of photon energy, $hν$⁠, and bandgap, E_g, was calculated by extrapolating the linear portion of the plot as shown in Fig. 3.

Table I summarizes the results. It was found that doping with different elements did not substantially change the bandgap energy of β-Ga₂O₃ crystals. The calculated E_g is less than the recently reported value of 4.9 eV; however, it is within the range reported for Ga₂O₃ between 4.4 eV and 5.1 eV. The reason behind the discrepancies in the reported values of E_g in Ga₂O₃ is not understood. However, high level of impurities may reduce the band edge. Our interest here is determining the band edge for accurate comparison of trap levels.

The glow curves of different samples where intensity of the luminescence is plotted as a function of temperature (°C) are shown in Figs. 4 and 5. Some glow curves, e.g., glow curve of Fe-doped Ga₂O₃, show several overlapping peaks from 0 °C to 220 °C. In order to analyze and calculate the activation energy, deconvolution of overlapping peaks is necessary. Horowitz and Yossian described different types of computerized glow curve deconvolution techniques that have been used to separate the peaks.²⁸ Varney et al. fitted the peaks using a combination of Gauss and Lorentz functions multiplied by a linear function.²⁰ In this study, a Gauss function in the form of

was used to decompose the overlapping peaks, where A and w are the fitting parameters. The sum of these Gaussian fitted peaks, which are symmetric in nature, match very well with the experimental convoluted curve. However, the fact that the peaks are broad in the higher temperature side indicates that second or higher order kinetic is most likely the case here and the “two heating rates” method which is only applicable for first order kinetics will produce large errors in the trap level calculations.

Figure 4 shows the separation of glow peaks using Gauss function and Fig. 5 shows the TL glow curves for different Ga₂O₃ samples that were constructed by plotting intensity of the luminescence as a function of temperature. Fe-doped β-Ga₂O₃ [Fig. 5(a)] exhibits four peaks at different temperatures associated with four deep level traps. The overlapping peaks indicate the presence of defect centers with close activation energies. The sample was annealed in air at 900 °C for 4 h. After that, TL spectroscopy was performed again; it was observed that the luminescence intensity decreases for every peak to some extent which could be explained due to a decrease in trap density or in recombination/luminescence centers. One possibility is that these traps are associated with oxygen vacancies and annealing in air filled them and reduced their concentrations. The other may be related to a decrease in luminescence centers as annealing may modify their charge state and transfer them to nonradiative recombination centers. This will be discussed in detail below with the TL emission graphs. The four trap levels for the Fe-doped sample are 0.620 eV, 0.694 eV, 0.722 eV, and 1.262 eV (Table II). Annealing slightly changed the defect activation energies to 0.620 eV, 0.679 eV, 0.610 eV, and 0.946 eV but did not completely remove any peak (Table III). It is an indication that air annealing probably modifies some defect structure by filling up oxygen vacancies. The glow curve in Fig. 5(a) shows that the undoped β-Ga₂O₃ sample has only three peaks and the first peak for the Fe-doped sample is absent. Activation energies for the traps in the undoped sample were found to be 0.633 eV, 0.495 eV, and 0.751 eV (Table IV). The origin of the first peak (at 37 °C) in the Fe-doped sample that is absent in the undoped samples must be associated with Fe dopants as doping with Fe introduces higher concentrations of Fe ions and a significant amount of new defect centers that act as traps and deep acceptors in Ga₂O₃. We thus assume that the peak at 37 °C is associated with this trap. Sn-doped β-Ga₂O₃ showed no glow peak, perhaps due to the absence of a radiative recombination center as Sn doping may quench the luminescence. However, it may also be due to the absence of defect centers that act as electron traps as the incorporation of Sn atoms in the lattice may lead to the formation of defect complexes as follows. Activated Sn dopant atoms in conductive single crystal β-Ga₂O₃:Sn are present as Sn⁴⁺, preferentially substituting for Ga at the octahedral site.¹ β-Ga₂O₃ often contains gallium and oxygen vacancies. Sn (Sn⁴⁺, Sn²⁺) might go into these gallium vacancies and change the charge state and electronic configuration of these defects. To see a glow peak in thermoluminescence, it is required that the metastable defects capture electrons at low temperature that is released later by thermal stimulation. The inability to capture electrons makes them “inactive” centers. We consider the second possibility because of the high conductivity of Sn doped samples shown below from Hall-effect measurements. The glow curve of the Mg-doped [Fig. 5(c)] sample has two distinct luminescence peaks where one has a much higher intensity. Besides, luminescence intensity differs with the difference in dopant concentration. The activation energy associated with the first strong peak was found to be 0.954 eV, and its intensity is much higher than that of EFG grown samples [Fig. 5(b)]. The activation energy of the second peak was hard to calculate because of the high level of noise.

Figure 6 shows the contour plots of TL emission in all samples where luminescence intensity is plotted as a function of wavelength and temperature illustrating the interaction between the traps and recombination centers. Different colors represent different ranges of intensity. The most obvious feature of these plots is that all defect levels give TL emission at around 700 nm irrespective of their activation energies or dopant nature. This indicates that only one recombination center associated with 700 nm emission is active and the released electrons from different traps recombine with the hole at this center or transfer their energy to it. In fact, this is common in many TL measurements and it happens when there is one strong recombination or luminescence center in the sample despite the presence of many trap levels. When the electrons are released from different trap levels, they simply transfer their energy to the same luminescence center. Figure 7 displays TL intensity as a function of wavelength at all temperature featuring the 700 nm peak shown in the contour plot in Fig. 6. This 700 nm red light emission is assumed to be related to Fe impurities as it is common that a very small amount of iron impurity led to an emission in many oxides between 700 and 1000 nm.²¹ The reduction of the intensity of all TL peaks of the Fe-doped sample after air annealing shown in Fig. 5 and discussed above could be in fact due to the reduction in active Fe luminescence centers as air annealing may modify their charge state and suppress their emission.

Gao et al.²⁹ used deep level transient spectroscopy (DLTS) to investigate deep level defects in β-Ga₂O₃ and reported several defect levels related to oxygen and gallium vacancies. Two deep levels for the as-grown samples investigated by thermoluminescence spectroscopy in this work (Table IV), located approximately at 0.62 and 0.75 eV below the conduction band minimum, match with those calculated by DLTS and surface photovoltage spectroscopy (SPS).²⁹ Ingebrigtsen et al.³⁰ also reported a defect level located at approximately 0.78 eV below the conduction band minimum. Fe_Ga, and not an intrinsic defect, was reported to be responsible for this deep level. Another deep level of ionization energy very close to the previous one, approximately 0.72 eV but originated from intrinsic defect, has also been reported in their investigation.³⁰ 

Hall-effect measurements were performed on the samples at room temperature, and the results are summarized in Table V. Sn-doped β-Ga₂O₃ showed substantially high conductivity and large carrier density. Sn dopant is known to act as a donor in β-Ga₂O₃. Fe-doped β-Ga₂O₃ was found to be semi-insulating with a resistivity of 5.10 × 10⁶ Ω cm and a carrier density of 2.25 × 10⁸ cm⁻³. Undoped β-Ga₂O₃ single crystals have lower resistivity than the Fe-doped sample but higher resistivity than the Sn-doped one with the resistivity of 1.29 × 10² Ω cm and carrier density of 2.51 × 10¹⁴ cm⁻³. The carriers in all samples were found to be electrons confirming the well-known dominant n type conductivity in Ga₂O₃.

By comparing trap level measurements and transport measurements, it can be concluded that the origins of the semi-insulating characteristics of Fe and Mg doped Ga₂O₃ are the increase of original defect centers that act as electron traps as well as the formation of new defect centers in case of iron doping. The Sn dopant may induce defect centers; however, these defects do not lead to TL emission.

Carrier dynamics, defect levels, and optical and electrical transport properties of β-Ga₂O₃ single crystals doped with several dopants and grown by EFG and CZ methods were investigated by thermoluminescence spectroscopy, optical absorption spectroscopy, and Hall-effect measurements. Four deep level traps for Fe-doped, three deep level traps for undoped, and two deep level traps for Mg-doped β-Ga₂O₃ single crystals were identified and their activation energies were calculated. It was found that the recombination centers are of the same nature, irrespective of dopant types or defect activation energies and are assumed to be related to iron impurities. The Sn-doped sample did not show any glow peak, and hence the absence of defect centers that act as electron traps or/and absence of a radiative recombination pathway is assumed. Sn doped samples exhibit high conductivity, while all other samples showed high resistivity at room temperature. TL data indicate that the high resistivity induced in semi-insulating Ga₂O₃ by Fe and Mg doping is due to the increase of native defect centers and the formation of new defect complexes that act as deep electron traps and substantially affect their transport. From optical absorption spectroscopy, it was found that the incorporation of dopants does not change the bandgap energy, but changes the transparency of the samples in the near IR and visible regions. This indicates that it is appropriate to compare the calculated defect levels among the samples.

We would like to thank Kelson Chabak, John Blevins, and Kevin Leedy at the Air Force Research Laboratory at Wright Patterson for providing samples. This work was supported as part of the “FUTURE”, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.